CN110212530A - N × N form dimension calculation method of power distribution network security domain - Google Patents
N × N form dimension calculation method of power distribution network security domain Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The present invention discloses a kind of N × N form dimension calculation method of power distribution network security domain, includes the following steps: the dimension for defining power distribution network security domain first: for there is the power distribution network of N feedback line, after considering feeder line communication relationship, being equivalent to NeThe full contact power distribution network of feedback line, wherein NeFeeder line number referred to as of equal value, defines the dimension of DSSR；Secondly the incidence matrix of power distribution network is generated；Then the row-column transform for making incidence matrix, obtains transformation matrix；It extracts cornerwise feeder line combination and extracts the feeder line combination in addition to diagonal lumped matrix；The virtual full contact structure for constructing power distribution network, obtains virtual portfolio；Finally calculate the dimension of power distribution network security domain.Present method solves existing method more difficult the problem of directly comparing DSSR scale.
Description
Technical field
The invention belongs to power distribution network security domain dimension computing technique fields, propose a kind of power distribution network based on correlation matrix
Security domain (DSSR) dimension calculation method.DSSR dimension is defined as most common N × N form by this method, can be facilitated than less
With the size of the DSSR problem scale of power distribution network.
Background technique
The concept of security domain was derived from transmission system, from proposition power transmission network Steady State Security Region in 1975[1]Afterwards, transmission of electricity security domain
Establish more complete theory[2-3].The following power distribution network intelligence degree will be more close with power transmission network[4-5], the peace of operation
Complete and efficiency requirements can also greatly improve, and the application of power distribution network security domain will be provided with condition and demand.Power distribution network security domain[6]
(Distribution SystemSecurity Region, DSSR), which is defined as power distribution network, can satisfy all of N-1 criterion
The closed set of operating point (operating status), and the existence of DSSR has passed through simulation observation[7], mathematical proof[8]And real example
Research[9]It is verified.DSSR has also gradually formed theoretical system, including concept definition in terms of fundamental research[8]、
Mathematical model[10]With property mechanism[7]Etc..But for the scale issue of DSSR, presently relevant research is also considerably less.
Text[11]It is put forward for the first time the concept of DSSR dimension, scale the problem of for indicating DSSR.DSSR is by theorem in Euclid space
Hyperplane surround[6], the corresponding security boundary constraint of each hyperplane, the quantity of variable is in different security boundaries constraints
Different, therefore DSSR dimension is defined using the dualistic manner of hyperplane number and variable number simultaneously.Although this definition can table
Show the scale of security domain, but there are clearly disadvantageous: firstly, dualistic manner does not meet the habit that people treat problem space；
Secondly, the scale of two DSSR problems can not be compared when the two count not of uniform size.Whether can with unitary mode come
Indicate the scale of DSSR problem?
Bibliography:
[1] Hnyilicza E, Lee S T Y, Schweppe F C.Steady-state security regions:
Set-theoretic approach [C] .Proc.PICA Conference, New Orleans:1975,347-355.
[2] Wu F F, Tsai Y K, Yu Y X.Probabilistic steady-state and dynamic
Security assessment [J] .Proceedings of the Csee, 1988,3 (1): 1-9.
[3] pragmatic solution [J] Proceedings of the CSEE of Zeng Yuan, Yu Yixin Dynamic Security Regions of Power Systems, 2003,
23 (5): 24-28.
[4] Guo Zhizhong Scheme of Self-healing Control Frame of Power Grid [J] Automation of Electric Systems, 2005,29 (10): 85-91.
[5] Liu H M, CHEN X Y, YU K, et al.The Control and Analysis of Self-
Healing Urban Power Grid [J] .IEEE Transactions on Smart Grid, 2012,3 (3): 1119-
1129.
[6] security domain models [J] the Automation of Electric Systems of Xiao Jun, Gu Wenzhuo, Wang Chengshan towards intelligent distribution system,
2013,37 (8): 14-19.
[7] Xiao Jun, Gong Xiaoxu, He Qibo wait intelligent distribution network N -1 security boundary topological property and Boundary algorithm [J]
Proceedings of the CSEE, 2014,34 (4): 545-554.
[8] Xiao Jun, motherland is strong, Bai Guannan, waits mathematical definition and existence proof [J] China of distribution system security region
Electrical engineering journal, 2016,36 (18): 4828-4836.
[9] Xiao Jun, motherland is strong, He Qibo, waits proof analysis [J] Automation of Electric Systems of power distribution network security domain,
2017,41 (3): 153-160.
[10] Xiao Jun, Su Buyun, Gong Xiaoxu wait power distribution network security domain models [J] the electric power of based on feeder interconnection relationship
System protection and control, 2015,43 (20): 36-44.
[11] Xiao Jun, Zhang Han, Zhang Baoqiang, wait dimension [J] Automation of Electric Systems of power distribution network security domain, and 2018,42
(1): 16-22.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of N × N form dimensions of power distribution network security domain
Calculation method redefines the dimension of power distribution network security domain, indicates dimension with most common N × N-dimensional form.
The present invention is the technical problem solved in background technique, the technical solution adopted is that proposing a kind of power distribution network security domain
N × N form dimension calculation method, include the following steps:
1) dimension of power distribution network security domain is defined: for there is the power distribution network of N feedback line, after considering feeder line communication relationship,
It is equivalent to NeThe full contact power distribution network of feedback line, wherein NeFeeder line number referred to as of equal value, defines the dimension of DSSR:
Dm=Ne×Ne(1)；
2) incidence matrix of power distribution network is generated；
3) row-column transform for making incidence matrix, obtains transformation matrix；
4) cornerwise feeder line combination is extracted；
5) the feeder line combination in addition to diagonal lumped matrix is extracted；
6) the virtual full contact structure for constructing power distribution network, obtains virtual portfolio；
7) it calculates the dimension of power distribution network security domain: being defined according to dimension, DSSR dimension wishes to be expressed as Ne×Ne, and Ne×
NeValue depend on n1A feeder line combination；
The dimension of one feeder line combination is exactly the feeder line number in combination, i.e. mi×mi, therefore n1The sum of the dimension of a feeder line combination
FormiFor the feeder line number of i-th of feeder line combination；
The dimension of virtual full contact structure is N × N, corresponding n2The dimension of a virtual portfolio, i.e.,mjIt is j-th
The feeder line number of virtual portfolio；
According to the corresponding relationship of quantity, there is following equation to set up:
Feeder line number N of equal value in DSSR dimensioneAre as follows:
After obtaining feeder line number of equal value, DSSR dimension D can be obtained by formula (1)m。
Preferably, the communication relationship between the step 2) feeder line can be divided into simply connected network, with it is close with it is remote, with close different remote, each other
It is close remote, close remote single-phase company, different closely with remote, different closely with remote 7 kinds, 4 relevance grades are classified as by the topology distance between feeder line；
Incidence matrix A=[amn] refer to the association etc. indicated between feeder line in power distribution network (or feeder line section) with matrix form
Grade, matrix element amnThe relevance grades of value foundation obtain, it is as follows:
Preferably, the step 3) transformation matrix need to meet following two condition: 1. matrix in block form diagonally is
Nonzero element；2. successively successively decreasing from upper left side to the order of lower right matrix in block form.
The utility model has the advantages that the invention proposes a kind of N × N form dimension definition of power distribution network security domain based on correlation matrix
And algorithm, existing DSSR dimension is improved, can it is more acurrate and easily reflection DSSR the problem of scale.
The representation method not only more meets the habit that people treat problem space, also solves the more difficult direct ratio of existing method
The problem of compared with DSSR scale.
Detailed description of the invention
Fig. 1 is simple example；
Fig. 2 is the virtual full contact structure of simple example；
Fig. 3 is complicated example schematic diagram；
Fig. 4 is the virtual full contact structure of complicated example；
Fig. 5 is the algorithm flow chart of DSSR dimension.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described further.
The definition of power distribution network security domain N × N form dimension and dimension algorithm based on feeder line incidence matrix, can consider
To after the communication relationship between feeder line, the real dimensions of security domain are obtained.
Whole process is divided into following seven step, and specific flow chart is shown in annex:
1. defining the dimension of power distribution network security domain
For there is the power distribution network of N feedback line, after considering feeder line communication relationship, it is equivalent to NeThe full contact distribution of feedback line
Net, wherein NeFeeder line number referred to as of equal value, defines the dimension of DSSR:
Dm=Ne×Ne (1)
2. generating the incidence matrix of power distribution network: the communication relationship between feeder line can be divided into simply connected network, with closely with remote etc. 7 kinds；This
Invention is classified as 4 relevance grades by the topology distance between feeder line, as shown in table 1.
1 feeder line communication relationship of table and relevance grades classification
Incidence matrix A=[amn] refer to the association etc. indicated between feeder line in power distribution network (or feeder line section) with matrix form
Grade, matrix element amnValue obtained according to the relevance grades of table 1, it is as follows:
It illustrates how to generate incidence matrix according to feeder line communication relationship by taking the simple example of Fig. 1 as an example.
Structure totally 9 feedback line in figure, 10 feeder line sections (Ti indicates that main transformer, Fj indicate feeder line section).Contact between feeder line is closed
System sees that annex, the incidence matrix of generation are shown in Table 2.
The incidence matrix A of the simple example of table 2
3. making the row-column transform of incidence matrix
Row-column transform is made to incidence matrix A, obtains transformation matrix T.Transformation matrix T need to meet following two condition:
1. matrix in block form diagonally is nonzero element；
2. successively successively decreasing from upper left side to the order of lower right matrix in block form.
For example, the transformation matrix of table 2 is shown in Table 3.
The transformation matrix T of the simple example of table 3
4. extracting cornerwise feeder line combination
Appoint from the power distribution network for having N feedback line and takes m feedback line, if any two feedback line is relevant in m feedback line, definition
The m feedback line constitutes a feeder line combination, is denoted as (F1,F2,…,Fm), 2≤m≤N.It is all non-by defining, in incidence matrix
The corresponding feeder line of the submatrix of neutral element constitutes a feeder line combination.
The upper left matrix in block form of transformation matrix T is known as the 1st matrix in block form, remaining matrix in block form is diagonally with such
Push away name.Terminate since the upper left corner to the lower right corner by matrix in block form, removes extractable outside lower right corner individual element matrix in block form
Obtain cornerwise r feeder line combinations1、s2、…、srAs
It counts and uses.
For example, diagonally sharing 3 matrixs in block form in table 3, remove outside the single element matrix in block form in the lower right corner, it is remaining
2 matrixs in block form (being shown in Table middle dash area) form 2 feeder line combinations (F1, F21, F22, F3, F6, F7) and (F5, F8, F9).
5. extracting the feeder line combination in addition to diagonal lumped matrix
Also there is nonzero element in remaining outer position of diagonal lumped matrix, and the corresponding feeder line of submatrix that they are generated also can structure
It is combined at feeder line.
Based on the 1st matrix in block form, non-zero is successively being looked for the right for unit with column in line number where the matrix in block form
Element, then the row where the nonzero element in same row and the column-generation one are all the submatrix of nonzero element, corresponding feedback
Line constitutes a feeder line combination.Then, it successively with the 2nd ..., based on r-th of matrix in block form, repeats the above steps,
Obtain all feeder line combinations in addition to diagonal lumped matrix.
For example, the 1st matrix in block form (F1, F21, F22, F3, F6, F7) of table 3 is 6 row, 6 array, have in preceding 6 row:
The nonzero element of 7th column F5 column is located at F3 and is expert at, and the nonzero element of the 8th column F8 column is located at F1, F21, F22, F3
Be expert at, the nonzero element of the 9th column F9 column is located at F21 and is expert at, the 10th nonzero element for arranging F4 column be located at F1,
F21, F22, F3 are expert at, therefore (F5, F3), (F8, F1, F21, F22, F3), (F9, F21), (F4, F1, F21, F22, F3) are respectively
Constitute a feeder line combination.2nd matrix in block form is (F5, F8, F9), is had in this 3 row: the non-zero entry of the 10th column F4 column
Element is located at F5, F9 and is expert at, therefore (F4, F5, F9) is a feeder line combination.
Finally, this two-part feeder line combination together constitutes the n of the power distribution network1A feeder line combination.
Fig. 1 network has n1=7 feeder line combinations: (F1, F21, F22, F3, F6, F7), (F5, F3), (F8, F1, F21,
F22,F3)、(F9,F21)、(F4,F1,F21,F22,F3)、(F5,F8,F9)、(F4,F5,F9)。
6. constructing the virtual full contact structure of power distribution network, virtual portfolio is obtained
One power distribution network containing N feedback line, finds n according to above-mentioned steps1A feeder line combination.For this power distribution network,
When it is to get in touch with entirely, the dimension one of power distribution network is set to N × N.Still according to n1Acquiring method seeks the combination of its feeder line, it is assumed that looks for
To n2It is a, by this n2A feeder line group is collectively referred to as getting in touch with virtual feeder line combination, abbreviation virtual portfolio entirely.
For example, the virtual full contact structure of Fig. 1 is shown in Fig. 2.
The incidence matrix of Fig. 2 is shown in Table 4, and ranks sequence and cornerwise matrix in block form divide identical as 3 matrix of table.
Diagonal line and the virtual portfolio in addition to diagonal lumped matrix are extracted respectively.
4 cornerwise 2 matrixs in block form of table formed virtual portfolio be (F1, F21, F22, F3, F6, F7) and (F5, F8,
F9)。
Subsequent 7th column to the 10th column each column of 1st matrix in block form are and preceding 6 row constitutes a virtual portfolio.2nd point
Subsequent 10th column of block matrix and its one virtual portfolio (F4, F5, F8, F9) of composition.
N can finally be obtained2=7 virtual portfolios: (F1, F21, F22, F3, F6, F7), (F5, F1, F21, F22, F3, F6,
F7)、(F8,F1,F21,F22,F3,F6,F7)、(F9,F1,F21,F22,F3,F6,F7)、(F4,F1,F21,F22,F3,F6,
F7)、(F5,F8,F9)、(F4,F5,F8,F9)。
The incidence matrix of the virtual full contact structure of table 4
7. calculating the dimension of power distribution network security domain
It is defined according to dimension, DSSR dimension wishes to be expressed as Ne×Ne, and Ne×NeValue depend on n1A feeder line combination.One
The dimension of a feeder line combination is exactly the feeder line number in combination, i.e. mi×mi, therefore n1The sum of the dimension of a feeder line combination isFor the feeder line number of i-th of feeder line combination；The dimension of virtual full contact structure is N × N, corresponding n2A virtual group
The dimension of conjunction, i.e.,mjFor the feeder line number of j-th of virtual portfolio.
According to the corresponding relationship of quantity, there is following equation to set up:
Feeder line number N of equal value in DSSR dimensioneAre as follows:
After obtaining feeder line number of equal value, DSSR dimension D can be obtained by formula (1)m。
For example, the feeder line combination and virtual portfolio arrangement by simple example are as follows, it is shown in Table 5.
The feeder line of the simple example of table 5 combines and virtual portfolio
The result sought substitution formula (2) is obtained:
Feeder line number N of equal value is obtained using formula (3)e=6.6, therefore the DSSR dimension D of power distribution networkm=6.6 × 6.6.
Embodiment
1, example basic condition
The grid structure of complicated example is (SPi indicates substation, and Tj indicates main transformer) as shown in Figure 3, totally 3 35kV power transformations
It stands, total capacity 56MVA；Totally 7 times 10kV feeder lines, capacity are 9MVA.There is a block switch in figure, totally 8 feeder line sections.
2, the implementation steps of the invention
1) according to the communication relationship between feeder line, the incidence matrix for generating complicated example is shown in Table 6.
The incidence matrix of the complicated example of table 6
2) row-column transform is made to 6 matrix of table, table 7 is obtained after transformation.
The transformation matrix of the complicated example of table 7
3) cornerwise feeder line combination: (F1, F71, F72), (F2, F3, F4) is extracted from table 7；It extracts and removes diagonal line piecemeal
Feeder line combination outside matrix: n finally can be obtained in (F5, F71, F72), (F2, F3, F6)1=4 feeder line combinations.
4) the virtual full contact structure of Fig. 3 is shown in Fig. 4.
The incidence matrix of Fig. 4 is shown in Table 8, and ranks sequence and cornerwise matrix in block form divide identical as 7 matrix of table.
The incidence matrix of the virtual full contact structure of table 8
Cornerwise virtual portfolio is extracted from table 8: (F1, F71, F72), (F2, F3, F4)；It extracts and removes diagonal line piecemeal square
Battle array outside virtual portfolio: (F1, F71, F72, F2), (F1, F71, F72, F3), (F1, F71, F72, F4), (F1, F71, F72,
F5)、
(F1, F71, F72, F6), (F2, F3, F4, F5), (F2, F3, F4, F6), (F5, F6), finally can be obtained n2=10
A virtual portfolio.
5) the feeder line combination of complicated example and virtual portfolio arrange as follows, are shown in Table 9.
The feeder line combination and virtual portfolio of the complicated example of table 9
Data are substituted into formula (2) to obtainFeeder line of equal value is obtained using formula (3)
Number Ne=4.1, therefore the DSSR dimension D of complicated examplem=4.1 × 4.1.
Annex
1, the algorithm flow chart of DSSR dimension:
2, the communication relationship between Fig. 1 feeder line:
The feeder line communication relationship of the simple example of table 10 is classified
Note: ' FX-FY ' indicates the communication relationship between feeder line FX and feeder line FY.Such as: ' F1-F6 ' indicates two feedback line F1
Communication relationship between F6, F1 and F6 is simply connected network as can be seen from Figure 1, therefore ' F1-F6 ' is categorized into simply connected network.
Claims (3)
1. N × N form dimension calculation method of power distribution network security domain, which comprises the steps of:
1) dimension of power distribution network security domain is defined: of equal value after considering feeder line communication relationship for there is the power distribution network of N feedback line
In NeThe full contact power distribution network of feedback line, wherein NeFeeder line number referred to as of equal value, defines the dimension of DSSR:
Dm=Ne×Ne(1)；
2) incidence matrix of power distribution network is generated；
3) row-column transform for making incidence matrix, obtains transformation matrix；
4) cornerwise feeder line combination is extracted；
5) the feeder line combination in addition to diagonal lumped matrix is extracted；
6) the virtual full contact structure for constructing power distribution network, obtains virtual portfolio；
7) dimension of power distribution network security domain is calculated:
It is defined according to dimension, DSSR dimension wishes to be expressed as Ne×Ne, and Ne×NeValue depend on n1A feeder line combination；
The dimension of one feeder line combination is exactly the feeder line number in combination, i.e. mi×mi, therefore n1The sum of the dimension of a feeder line combination ismiFor the feeder line number of i-th of feeder line combination；
The dimension of virtual full contact structure is N × N, corresponding n2The dimension of a virtual portfolio, i.e.,mjIt is virtual for j-th
Combined feeder line number；
According to the corresponding relationship of quantity, there is following equation to set up:
Feeder line number N of equal value in DSSR dimensioneAre as follows:
After obtaining feeder line number of equal value, DSSR dimension D can be obtained by formula (1)m。
2. N × N form dimension calculation method of power distribution network security domain according to claim 1, which is characterized in that the step
Communication relationship between rapid 2) feeder line can be divided into simply connected network, with it is close with it is remote, with nearly different remote, close each other remote, close remote single-phase company, different close same
Far, different closely with remote 7 kinds, 4 relevance grades are classified as by the topology distance between feeder line；
Incidence matrix A=[amn] refer to and indicate relevance grades between feeder line in power distribution network (or feeder line section), square with matrix form
Array element element amnThe relevance grades of value foundation obtain, it is as follows:
3. N × N form dimension calculation method of power distribution network security domain according to claim 1, which is characterized in that the step
Rapid 3) transformation matrix need to meet following two condition: 1. matrix in block form diagonally is nonzero element；2. from upper left side to
The order of lower right matrix in block form successively successively decreases.
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| CN107590748A (en) * | 2017-08-17 | 2018-01-16 | 天津大学 | A kind of full dimension observation procedure of power distribution network security domain |
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| CN105552890A (en) * | 2015-12-23 | 2016-05-04 | 天津大学 | Security region volume based evaluation method for distribution system N-1 safe operation range |
| CN107147108A (en) * | 2017-05-09 | 2017-09-08 | 天津大学 | A kind of computational methods of distribution system security region dimension |
| CN107590748A (en) * | 2017-08-17 | 2018-01-16 | 天津大学 | A kind of full dimension observation procedure of power distribution network security domain |
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